pure and applied geophysics

, Volume 142, Issue 3–4, pp 567–585 | Cite as

The propagation of a single shear crack: A displacement discontinuity model

  • J. -Cl. De Bremaecker
  • K. Wei
Earthquake Source Mechanics and Fracture Mechanics: Theory and Observation


Numerical studies using the displacement discontinuity method show that a single shear crack under compression propagates in its own direction, because such propagation results in the maximum release of strain energy. The methods of linear elastic fracture mechanics may not be used for such a closed crack, and the stress intensity factors are meaningless in that case. Laboratory observations of propagation by means of “kinks” at an angle of approximately 70° to the crack may be due to heterogeneities, to the effect of a preexisting crack, to end effects, to microcracking, or to some combination of these factors. Such kinks may thus be local phenomena which cannot release most of the strain energy, and are not incompatible with our numerical results which are based on a global energy balance.

Key words

Crack propagation fracture propagation boundary element method 


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  1. Adam, C., andAfzali, M.,Study of three-dimensional crack front shape by boundary elements method. InProc. 7th Int. Conf. Boundary Elements (eds. Brebbia, C. al. 1985) pp. 8–27 to 8–46.Google Scholar
  2. Aliabadi, M. H., andRooke, D. P.,Numerical Fracture Mechanics (Kluwer Acad. Publ., Boston 1992).Google Scholar
  3. Antes, H., andPanagiotopoulos, P. D.,The Boundary Integral Approach to Static and Dynamic Contact Problems (Birkhäuser Verlag, Boston 1992).Google Scholar
  4. Becker, E. B., Carey, G. F., andOden, J. T. Finite Elements An Introduction (Prentice-Hall, Englewoods Cliffs, NJ 1981).Google Scholar
  5. Brace, W. F. (1960),An Extension of the Griffith Theory of Fracture of Rocks, J. Geophys. Res.,65, 3477–3480.Google Scholar
  6. Brace, W. F., andBombolakis, E. G. (1963),A Note on Brittle Crack Growth in Compression, J. Geophys. Res.68, 3709–3713.Google Scholar
  7. Cornet, F. H. (1979),Comparative Analysis by the Displacement-discontinuity Method of Two Energy Criteria for Fracture, J. Appl. Mech.,46, 349–355.Google Scholar
  8. Crouch, S. L., andStarfield, A. M.,Boundary Element Methods in Solid Mechanics (George Allen and Unwin 1983).Google Scholar
  9. Cruse, T. A.,Boundary Element Analysis in Computational Fracture Mechanics (Kluwer Acad. Publ., Boston 1988).Google Scholar
  10. Erdogan, F., andSih, G. C. (1963),On the Crack Extension in Plates under Plane Loading and Transverse Shear, Am. Soc. Mech. Eng., J. Basic Engr.85, 519–527.Google Scholar
  11. Freund, L. B.,Dynamic Fracture Mechanics (Cambridge Univ. Press 1990).Google Scholar
  12. Fung, Y. C.,Foundations of Solid Mechanics (Prentice-Hall, Englewood Cliffs, NJ 1965).Google Scholar
  13. Gdoutos, E. E.,Fracture Mechanics Criteria and Applications (Kluwer Acad. Publ., Boston 1990)Google Scholar
  14. Griffith, A. A. (1921),The Phenomena of Rupture and Flow in Solids, Phil. Trans. Roy. Soc. LondonA 221, 163–198.Google Scholar
  15. Handin, J. (1969),On the Coulomb-Mohr Failure Criterion, J. Geophys. Res.74, 5343–5348.Google Scholar
  16. Hoek, E., andBienawski, Z. T. (1984),Brittle Fracture Propagation in Rock under Compression, Int. J. Fract. Mech.1, 135–155.Google Scholar
  17. Horii, H., andNemat-Nasser, S. (1985),Compression-induced Microcracks Growth in Brittle Solids: Axial Splitting and Shear Failure, J. Geophys. Res90, 3105–3125.Google Scholar
  18. Horii, H., andNemat-Nasser, S. (1986),Brittle Failure in Compression: Splitting, Faulting and Brittle-ductile Transition, Phil. Trans. Roy. Soc. LondonA, 319, 337–374.Google Scholar
  19. Huang, J., Chen, G., Zhao, Y., andWang, R. (1990),An Experimental Study of the Strain Field Development Prior to Failure of a Marble Plate under Compression, Tectonophysics175, 269–284.Google Scholar
  20. Hussain, M. A., Pu, S. L., andUnderwood, J. H.,Strain energy release rate for a crack under combined Mode I and Mode II. InFracture Analysis (Am. Soc Testing Materials, Spec. Techn. Publ.560, 1974) pp. 1–28.Google Scholar
  21. Ingraffea, A. R.,Numerical modelling of fracture propagation. InRock Fracture Mechanics (Ross-manith, H. P., ed.) (Springer-Verlag 1983) pp. 152–208.Google Scholar
  22. Ingraffea, A. R.,Fracture propagation in rock. InMechanics of Geomaterials (Bazant, Z., ed.) (J. Wiley and Sons, 1985) pp. 219–258.Google Scholar
  23. Ingraffea, A. R.,Theory of crack initiation and propagation in rock. InFracture Mechanics of Rock (Atkinson, B. K., ed.) (Academic Press, New York 1989) pp. 71–110.Google Scholar
  24. Irwin, G. R. (1957),analysis of Stresses and Strains near the End of a Crack Traversing a Plate, J. Appl. Mech.,24, 361–364.Google Scholar
  25. Irwin, G. R., Kies, J. A., andSmith, H. L. (1958),Fracture Strengths Relative to Onset and Arrest of Crack Propagation, Proc. Am. Soc. Testing Mat.,58, 640–660.Google Scholar
  26. Kanninen, M. F. andPopelar, C. H.,Advanced Fracture Mechanics (Oxford Univ. Press 1985).Google Scholar
  27. Lawn, B. R., andWilshaw, T. R.,Fracture of Brittle Solids (Cambridge Univ. Press, New York 1975).Google Scholar
  28. Lemaitre, J. (1976),Extension de la notion de taux d'énergie de fissuration aux problèmes tridimensionels et non linéaires, C. R. Acad. Sci. ParisB 282, 157–160.Google Scholar
  29. Lin, J., andParmentier, E. M. (1988),Quasistatic Propagation of a Normal Fault: A Fracture Mechanics Model, J. Struct. Geol.,10, 249–262.Google Scholar
  30. Mandl, G.,Mechanics of Tectonic Faulting (Elsevier, New York 1988).Google Scholar
  31. McClintock, F. A., andwalsh, J. B.,Friction of Griffith cracks in rocks under pressure. InProc. Conf. 4th U. S. Nat. Congr. Appl. Mech (Am. Soc. Mech. Engineers 1962) pp. 1015–1021.Google Scholar
  32. Melin, S. (1987),Fracture from a Straight Crack Subjected to Mixed-mode Loading, Int. J. Fract.32, 257–263.Google Scholar
  33. Nemat-Nasser, S., andHorii, H. (1982),Compression-induced Nonplanar Crack Extension with Application to Splitting, Exfoliation, and Rockburst, J. Geophys. Res.,87, 6805–6821.Google Scholar
  34. Scavia, C. (1992),A Numerical Technique for the Analysis of Cracks Subjected to Normal Compressive Stresses, Int. J. Num. Methods Eng.,33, 929–942.Google Scholar
  35. Scholz, C. H.,The Mechanics of Earthquakes and Faulting (Cambridge Univ. Press 1990).Google Scholar
  36. Scholz, C. H., andAviles, C. A.,The fractal geometry of faults and faulting. In.Earthquake Source Mechanics (eds. Das, S.,et al. (Am. Geophys. U., Geophys. Monograph37, 1986) pp. 147–155.Google Scholar
  37. Virieux, J., andMadariaga, R. (1982)Dynamic Faulting studied by a Finite-difference Method, Bull. Seismol. Soc. Am.,72, 345–369.Google Scholar
  38. Wei, K., andDe Bremaecker, J. Cl (1992),A Replacement for the Coulomb-Mohr Fracture Criterion, Geophys. Res. Letters,19, 1033–1036.Google Scholar
  39. wei, K., andDe Bremaecker, J. Cl. (1993a),A Computational Scheme for Frictional Contact Problems (in preparation).Google Scholar
  40. Wei, K., andDe Bremaecker, J. C. (1993b),Fracture Growth under Compression, J. Geophys. Research (in press).Google Scholar
  41. Wei, K., andDe Bremaecker, J. C. (1993c),Fracture under Compression. The Direction of Initiation, Int. J. Fracture,61, 267–294.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • J. -Cl. De Bremaecker
    • 1
  • K. Wei
    • 1
  1. 1.Department of Geology and GeophysicsRice UniversityHoustonUSA

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